Conventional (MR) images are reconstructed by Fourier transformation of a limited number of phase-encoded signals in the center of k-space. Generally there is a tradeoff between imaging time and spatial resolution since these attributes are influenced in conflicting ways by the number of phase-encodings. For example, to decrease imaging time, the number of phase-encodings has to be decreased, thereby causing truncation artifacts and poor resolution of the reconstructed images. To obtain higher spatial resolution and reduce truncation artifacts, it is generally necessary to measure more phase-encoded signals, thereby lengthening acquisition time.
Several investigators have proposed constrained image reconstruction schemes which reduce truncation artifacts in MR images without acquiring more phase-encoded signals. Generally constrained imaging methods seek to use previous experience with the imaging of certain types of objects to enhance the subsequent imaging of similar objects. In each case, a small number of phase-encoded signals in the center of k-space are measured, and prior information about image content was used to estimate high-k image components. Some of these schemes use mathematical hypotheses about image edge structure in order to estimate high-k signals from the measured low-k data. For example, Haacke et al. in an article entitled "Constrained reconstruction: A superresolution, optimal signal-to-noise alternative to the Fourier transform in magnetic resonance imaging," Medical Physics, Vol. 16, No. 3, May/Jun. 1989, fits the low resolution data with a parametric "box car" model which does not have truncation artifacts.
Constable and Henkelman in an article entitled "Data Extrapolation for Truncation Artifact Removal," Magnetic Resonance in Medicine, vol. 17, 1991, begin with a low resolution image produced by conventional Fourier transformation of the measured phase-encoded signals. The image was filtered to smooth out Gibbs "ringing" and then subjected to edge enhancement. High-k components of the object were estimated from the inverse Fourier transformation of this processed image. The final image was reconstructed by Fourier transformation of an array consisting of the measured signals in the center of k-space and the estimated high-k Fourier components.
Other investigators proposed ways of using highly resolved anatomic images to constrain the reconstruction of a chemical shift image or functional image of the same cross-section. These methods were based on the feeling that spectroscopic or functional images should resemble anatomic images in some sense. For example, Hu and Stillman in an article entitled "Technique for Reduction of Truncation Artifact in Chemical Shift Images," IEEE Nuclear Science Symposium, Medical imaging Conference, Oct. 22-27, 1990, propose a technique for reducing truncation artifacts in chemical shift images by using boundary information available from anatomical images. This method of estimating high-k components is similar to that of Constable and Henkelman, except that edges in anatomic images are utilized to guide the smoothing of truncation artifacts in the chemical shift data.
Another method, such as that disclosed by Liang and Lauterbur in an article entitled "A Generalized Series Approach to MR Spectroscopic Imaging," IEEE Tran. on Medical Imaging, Vol. 10, 1991, proposes a method of reconstructing temporally-varying functional images from an anatomical image and a small number of phase-encoded signals. Specifically, each functional image is approximated by the product of a previously-measured high resolution anatomical image and a time dependent image with only a few spatial components. The latter may be estimated from a small number of phase-encoded signal measurements. Other methods acquired an initial high resolution anatomical image of the region of interest. Subsequent functional images of the region were reconstructed from a few measured phase-encoded signals in the center of k space together with high-k components copied from the initial high resolution image.
All of these methods were shown to offer an advantage in at least some imaging situations. However, each method depends on specific assumptions about image edge content or about the correlation between different types of images of the same cross section. In each case, this assumption is based on the author's intuition about which features should be incorporated in the final images. In any imaging situation, it is difficult to know if such a constraint is applicable. A problem arises if the user's intuition is wrong and an inappropriate constraint is applied, the resulting images could be degraded by peculiar artifacts which may be difficult to recognize.
Consequently there exists a need for a method and apparatus for obtaining images of an object which is not based on the user's intuition about what the final image should look like and which constraints should be applied to achieve that "look". Furthermore, there exists a need for an improved method and apparatus which does not suffer from the above limitations and which generates a high resolution image in a relatively short period of time.